Results 281 to 290 of about 1,210,874 (307)

Convolution sums of a divisor function for prime levels

International Journal of Number Theory, 2020
Recently, many identities for the convolution sum [Formula: see text] of the divisor function [Formula: see text] have been obtained since Royer obtained by the theory of quasimodular forms.
Bumkyu Cho
semanticscholar   +1 more source

A MONOTONIC CONVOLUTION FOR MINKOWSKI SUMS [PDF]

International Journal of Computational Geometry & Applications, 2007
We present a monotonic convolution for planar regions A and B bounded by line and circular arc segments. The Minkowski sum equals the union of the cells with positive crossing numbers in the arrangement of the convolution, as is the case for the kinetic convolution.
Victor Milenkovic, Elisha Sacks
openaire   +1 more source

Shifted convolution sums for higher rank groups

Forum mathematicum, 2018
In this paper, we study some shifted convolution sums for higher rank groups. In particular, we establish an asymptotic formula for a GL ⁢ ( 4 ) × GL ⁢ ( 2 ) {\mathrm{GL}(4)\times\mathrm{GL}(2)} shifted convolution sum ∑ n ≤ x | λ f ⁢ ( n ) | 2 ⁢ r l ⁢ (
Yujiao Jiang, G. Lü
semanticscholar   +1 more source

Evaluation of the convolution sums ∑l+27m=nσ(l)σ(m) and ∑l+32m=nσ(l)σ(m)

, 2016
We determine the convolution sums ∑l+27m=nσ(l)σ(m) and ∑l+32m=nσ(l)σ(m) for all positive integers n. We then use these evaluations together with known evaluations of other convolution sums to determine the numbers of representations of n by the octonary ...
S. Alaca, Yavuz Kesicioğlu
semanticscholar   +1 more source

Evaluation of the convolution sums ∑ak+bl+cm=nσ(k)σ(l)σ(m) with lcm(a,b,c) = 7,8 or 9

International Journal of Number Theory, 2017
It is known that the generating functions of divisor functions are quasimodular forms of weight [Formula: see text]. Hence their product is a quasimodular form of higher weight.
Y. Park
semanticscholar   +1 more source

Evaluating binomial convolution sums of divisor functions in terms of Euler and Bernoulli polynomials

, 2017
In this paper, we provide two identities about binomial convolution sums of σr♭(n; N/4,N) with N/4 ∈ ℕ, which are expressed in terms of Euler and Bernoulli polynomials.
Bumkyu Cho, Ho Park
semanticscholar   +1 more source

Evaluation of some convolution sums and representation of integers by certain quadratic forms in 12 variables

, 2017
In this paper, the convolution sums ∑i+12j=nσ(l)σ3(m), ∑3i+4j=nσ(l)σ3(m), ∑4i+3j=nσ(l)σ3(m) and ∑12i+j=nσ(l)σ3(m) are evaluated for all n ∈ ℕ, and their evaluations are used to determine the number of representation of a positive integer n by the forms ...
B. Köklüce, Hasan Eser
semanticscholar   +1 more source

Sums of Convolution Operators

SIAM Journal on Mathematical Analysis, 1972
Let $\Omega $ be an open set in $R_n $ and let $\mathcal{E}(\Omega )$ denote the space of infinitely differentiable functions on $\Omega $. Necessary and sufficient conditions are exhibited for a family $\{ \Omega _i \} _{i = 1}^N $ of open sets in $R_n$ and a family $\{ S_i \} _{i = 1}^N \subset \mathcal{E}'(R_n )$ in order that the convolution ...
openaire   +2 more sources

Sums with convolutions of Dirichlet characters

manuscripta mathematica, 2010
We bound short sums of the form \({\sum_{n\le X}(\chi_1{*}\chi_2)(n)}\), where χ1*χ2 is the convolution of two primitive Dirichlet characters χ1 and χ2 with conductors q1 and q2, respectively.
William D. Banks, Igor E. Shparlinski
openaire   +2 more sources

A generalization of regular convolutions and Ramanujan sums

The Ramanujan Journal, 2020
Regular convolutions of arithmetical functions were first defined by Narkiewicz (Colloq Math 10:81–94, 1963). Useful identities regarding generalizations of the totient-counting function and Ramanujan sums were later proven for regular convolutions by McCarthy (Port Math 27(1):1–13, 1968) and Rao (Studies in arithmetical functions, PhD thesis, 1967 ...
Joseph Vade Burnett, Otto Vaughn Osterman   +1 more
openaire   +2 more sources